The Geometry of mass

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We have shown throughout The Road to Unificationand its companion book “The Reality of the Fourth *Spatial* Dimension” there would be several theoretical advantages to defining the universe in terms of four *spatial* dimensions instead of four-dimensional space-time.

One is that it would allow physicists to derive the causality of mass by extrapolating the laws of a three-dimensional environment to fourth *spatial* dimension.

For the past 25 years, the Standard Model of particle physics has given us a complete mathematical description of the particles and forces that shape our world.  It predicts with so much accuracy the microscopic properties of particles and the macroscopic ones of stars and galaxies that many physicists feel that it is the ultimate theory of matter and energy.

But as Charles Seife mentions on page 142 of his book:

Alpha & Omega “Taken literally the plain vanilla form of the Standard model of particle physics does not say anything about particle mass at all: in fact if theorists try to put mass in to the equations of that model the equations blowup and become meaningless.”

However, one of the most observable properties of particles is that they have mass.  Therefore, if the Standard Model is the ultimate theory of particles, as many physicists believe you would think that it should be able to define or at least incorporate that observation into its theoretical structure.  The fact it cannot, as mentioned in Charles book, is a reason to look beyond it for a deeper understand of our universe.

One reason why it has been so difficult to understand the casualty of mass may be because Einstein only told us that how gravity “may act upon another at a distance through a vacuum” by extrapolating the physical image of how objects move on a curve surface in a three-dimensional environment to a curved four dimensional space-time manifold. This allowed him to conceptually understand gravity in terms of a physical image based on our three-dimension world.   
 
However he was unable to tell us what mass is, he was only able tell us how it interacts with space-time.

As Steven Weinberg said “Mass tells space-time how to curve while space-time tells mass how to move. 

This is similar to Newton in that he was able to mathematically define how mass gravitational interacts with other masses but was unable to understand or define a physical mechanism that could account for that interaction.

In other words the mathematics developed by Newton was only able to quantitatively predict gravitational forces while Einstein gave us the ability to conceptually understand why “one body may act upon another at a distance” by physically connecting it to the reality of what we can see and touch.

However Einstein’s and modern scientist’s inability to define or derive the casualty of mass can be traced to the fact that they chose to define the universe in terms of energy instead of mass.

Yet he gave us the ability to rectify this when he defined the geometric properties of a space-time universe and the dynamic balance between mass and energy in terms of the equation E=mc^2 and the constant velocity of light because it allows one to redefine a unit of time he associated with energy in his space-time universe to unit of space associated with mass in a universe consisting of only four *spatial* dimensions.

However changing ones perspective on the geometric structure of the universe form one of space-time to four *spatial* dimensions, as was just shown to be possible gives one the ability to define the physical mechanism by which mass created and why it is quantized in particles in terms of a physical image formed in our three-dimensional environment.

For example one can form a physical image of why energy is quantized, as was done in the article ” Why is energy/mass quantized? ” Oct. 4, 2007″ by extrapolating the image of a wave and its resonant properties in three dimension environment to one made up of four *spatial* dimensions. This would be analogous to how Einstein, as mentioned earlier was able to explain gravity by extrapolating the physical image of how objects move in a three-dimension space to one consisting of four dimensional space-time.

(Louis de Broglie was the first to predict the existence of the wave properties of mass when he theorized that all particles have a wave component. His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer).

Briefly that article showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would be meet in one consisting of four.

The existence of four *spatial* dimensions would give a matter wave that Louis de Broglie associated with a particle the ability to oscillate spatially on a “surface” between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital. This would force the “surface” of a three-dimensional space manifold to oscillate with respect to a fourth *spatial* dimension at a frequency associated with the energy of that event.

However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or “structure” to be established in four *spatial* dimensions.

Classical mechanics tells us that resonant systems can only take on the discrete or quantized energies associated with a fundamental or a harmonic of their fundamental frequency

Therefore, these resonant systems in a four *spatial* dimensions would define mass and its quantum mechanical properties in terms of the field properties of four space dimension because of the fact that the volumes of space containing them would have a higher concentration of energy and therefore their mass would be relative greater than the neighboring volumes.

However, one can also use the field properties Einstein would have associated with four *spatial* dimension to define the physical boundary of the mass component of a particle.In classical physics, a point on the two-dimensional surface of paper is confined to that surface. However, that surface can oscillate up or down with respect to three-dimensional space.

Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate “up” or “down” with respect to a fourth *spatial* dimension.

In other words the mass is a result of the confinement caused by the “upward” and “downward” oscillations of a three-dimension volume with respect to a fourth *spatial* dimension which concentrates the energy associated with a particle in the article “Why is energy/mass quantized?“.

As was shown earlier the symmetry of Einstein’s mathematics means that not only can one define the physical properties of particles in terms of four dimensional space-time but also in four *spatial* dimensions.

In other words one can understand how the wave energy associated with a particle can become confined and concentrated in the volume of space to create mass by, as was demonstrated earlier extrapolating the physical properties field properties of three dimension space to either four dimensional space-time or fourth spatial dimensions.

Latter Jeff

Copyright Jeffrey O’Callaghan  2009

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